They didn't seem to understand that the iPod is replaced, not sent back with a new battery.
Not necessarily... Not all 1st gen iPod nanos are part of the recall. That's why you are asked to enter the iPod's serial number. It's possible that before the recall was initiated, some 1st gen iPod nanos had the faulty battery replaced with a good one when the customer had a problem under warranty. Also, in the early days of the recall, when the available iPod nano was still the 1st gen model (or Apple still had stock of 1st gen models with a good battery), customers would have had their faulty 1st gen iPod nano replaced with a good 1st gen iPod nano, and that good 1st gen iPod nano would not be part of the recall. And it's possible that a later batch of 1st gen iPod nano had good batteries from the factory, and are not part of the recall.
The representative was just using the serial number database, to see if your 1st gen iPod nano was part of the recall. Apparently, it is not...